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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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11. The effect of transformations of scale on the mean and standard deviation

You just completed a small research project for your psychology class concerning the effects of an event that happened three years ago on women’s opinions and actions today.

The mean age of participants in your study is 20.1 years with a standard deviation of 2.7 years. As you write up your results, you realize that what matters is the ages of the participants three years ago when the event happened, not their ages now. You decide to subtract 3 from each of your participants’ ages. After you subtract 3 years, the mean age in your sample is blank years. The new standard deviation of the ages in your sample is blank years.

One of the variables you collected was the study participants’ heights in centimeters. The mean height of participants in your study is 165.4 centimeters with a standard deviation of 8.27 centimeters. Your professor, however, requested that you report this value in inches. To convert from centimeters to inches, you multiply by 0.394. After you multiply the heights of your participants by 0.394, the mean height in your sample is blank inches. The new standard deviation of the heights in your sample is blank inches.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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